Diamond wire sawing with narrower kerf losses and thinner as-cut wafers is a critical technology to further reduce wafering costs in the semiconductor industry. Nevertheless, as the scale of the wire web decreases, the effect of the liquid bridge formed by the capillary condensation of the cutting fluid between the diamond wires becomes significant. Moreover, the transverse wire vibration reduces the wire web gap at certain moments, which makes it easier for the wires to adhere to each other after wetting, thus hindering the slicing process. Therefore, a dynamical model for a double-wire system with liquid bridge action was developed in this study based on the transverse vibration theory of a diamond wire under support excitations to reveal the action mechanism of the liquid bridge between diamond wires. The dynamic adhesion process between the diamond wires moving with the supports is discussed. The effects of the guide wheel manufacturing error and the sawing parameters on the critical gap for spontaneous adhesion between the diamond wires are analyzed. The results show that the static double-wire system does not generate spontaneous adhesion when the surface gap of the wires is between the critical gap for spontaneous adhesion and the maximum adhesion gap. The support excitation causes the transverse wire displacement, which increases the critical gap for spontaneous adhesion to increase the risk of wires adhesion. The critical gap for spontaneous adhesion increases with increases in the guide wheel manufacturing error and the wire span as well as the wire speed and decreases with increases in the wire groove diameter and the wire tension. When the manufacturing error is doubled, the critical gap for spontaneous adhesion will increase more than twice this error increment. Strict control of the guide wheel manufacturing error is the most effective way of reducing the risk of wires adhesion during processing. Increases in the guide wheel diameter and decreases in the wire span and the wire speed within a reasonable range, or enhancing the mechanical properties of the wire to improve its breaking force, also help to reduce the critical gap for spontaneous adhesion.